lecture 13: magnetic sensors & actuatorsmech466/mech466-lecture-13.pdfmagnetic field is removed,...

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MECH 466Microelectromechanical Systems

University of VictoriaDept. of Mechanical Engineering

Lecture 13:Magnetic Sensors & Actuators

© N. Dechev, University of Victoria

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Magnetic Fields

Magnetic Dipoles

Magnetization Hysteresis Curve

Lorentz Force

Current Carrying Wires

Overview


Magnetic fields and forces can be used to actuate micro-scale devices, or be used to create novel micro-sensors.

Applications include:

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Magnetic Sensing and Actuation


Micro-Inductors andMicrocoils [N. Dechev]

Micro-Sensors(Resonant magnetometer withCMOS) [B. Eyer, K. Pister, et al]

Self-Assembly of Microstructures[C. Liu, J. E. Schutt-Aine]

Magnetic fields can arise in two main ways:

(A) Motion of Charge

(B) Magnetic Materials

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Review: Basics of Magnetism


Magnetic Field around a moving “Positive Charged” Particle[MIT TEAL/Studio Physics Project]

Magnetic Field around a Bar Magnet[Wikipedia]

A current-carrying conductor such as a wire, will induce a magnetic field around it, as follows:

Where: H is the ‘magnetic field intensity’.

Note: You can use the ‘right hand rule’ to determine the orientation of the magnetic field around the conductor. (Right Hand Rule: Imagine grasping the wire conductor, with your thumb pointing in the direction of the current, and note that your fingers curl in the direction of the magnetic field.)

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Magnetism Due to Moving Charge


Current Flow

Hi

H

Front View(Current moving “Out of Page”)

Magnetic fields also arise in permanent ferromagnets, also known as “hard” magnets.

Any piece of magnetic material is comprised of many ‘magnetic dipoles’:

For magnetic materials in a natural or raw state, these magnetic dipoles may be unaligned:

- Therefore, there is little or ‘no net’ magnetic field

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Magnetism Due to Magnetic Materials


Image of ‘un-aligned’ magnetic dipoles within a material.

Creation of permanent magnets:

(1) An appropriate hard-magnetic material is elevated to a high temperature, and subjected to a very strong external magnetic field.

(2) Due to the elevated temperature, the magnetic dipoles move easily, and align approximately with the magnetic field.

(3) The temperature is then reduced, and the magnetic dipoles become “frozen” in their aligned positions. The external magnetic field is removed, leaving the ‘magnetized’ material.

(4) The dipoles remain aligned to a high degree at all times, thereby creating a permanent magnetic field.

In “soft magnets” the dipoles are normally un-aligned, and must be driven into alignment by an external magnetic field H, to induce a further magnetic field by the soft magnet.

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The “magnetic field density”, B, inside a piece of magnetic material is measured in units of:

The “magnetic field density” is also known as the ‘magnetic induction’ or the ‘magnetic flux density’.

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H is defined as the “magnetic field intensity” and describes a magnetic field in space, which is measured in units of:

A good analogy to H, is the electric field E.

The relationship between B and H is presented as:

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Difference Between B and H Fields


Lets define B ‘more generally’ as: the “magnetic field density” within any material or within any medium.

In this sense, either B or H can be used to describe any magnetic field. ** Even if the B field is in air, or in empty space.**

Where as B is ‘related to the medium properties’, while H is not. 10

Difference Between B and H Fields


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Fig. 8.1 Magnetization Hysteresis Curve [C. Liu]

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Fig. 8.2 Magnetization Hysteresis Curve [C. Liu]

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Example Using: Magnetization Hysteresis Curve


See Class Notes

The ‘Lorentz Force’ arises as a charged body moves through a magnetic field, and is governed by:

This equation can be simplified for a one-dimensional case, as:

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Lorentz Force


Where: F - Force Matrix q - total charge of body v - Velocity Matrix of body B - Magnetic Field Matrix

Where: F - Force q - total charge of body v - Velocity of body B - Magnetic Field θ- Angle between B Field and v

The ‘Lorentz Force’ acts on a stationary wire that carries current, while that wire is in a magnetic field. Think of the current as the moving charge. Therefore, the force can be derived as:

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Lorentz Force on a Current-Carrying Wire


Where: i - Current in wire L - Length of wire

- Note, the derivation was done using the expression qv = iL where: q - Total charge v - Velocity

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[Fig. 8.3 from ‘Foundations of MEMS’, Chang Liu]

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Example: Lorentz Force on a Current-Carrying Wire


See Class Notes

When a conductor is moved through a magnetic field, a current will arise (will be induced) in the conductor.

This is the principle of electromagnetic induction, and is described by Faraday’s Law:

This general equation can be simplified to:

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Electromagnetic Induction


Where: E - Electric Field dL - an infinitesimal element of the contour C B - Magnetic Field Density dA - an infinitesimal area of the surface S where contour C and surface S are related by the right hand rule

Where: emf - Electromotive Force (in units of Volts) A - Area through which magnetic flux passes ϕ - angle between a vector perpendicular to the area A, and the magnetic field direction

In the case of a conductor (such as a wire), that is forced to move through a magnetic field, we can re-write the equation as:

To find the current, i, that is induced in the conductor, we need to know the resistance, R, of the conductor, and can write the expression:

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Electromagnetic Induction


Where: emf - Voltage across Conductor L - Length of the Conductor v - Velocity of the Conductor where B and v are related by the right hand rule

Conductor, Length L

B Field

ConductorVelocity v

When the conductor is moved through the magnetic field, a force will arise to maintain the conservation of energy ‘Lenz’s Law’.

When the conductor is moved with a velocity v as shown, a current will be induced. Due to this current, a Lorentz force FL will arise as shown in the diagram, in red. Therefore, a force F will arise to counteract this force, as described by:

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Electromagnetic Induction Forces


Where: it is assumed that B and v are at 90 degrees B Field

ConductorVelocity v

Current i

Force F

LorentzForce FL

There are three ways an emf can be induced in a loop:- Changing the magnetic field- Changing the area of the loop- Changing the angle between the field and the loop

emf in loop will only occur during a changeof one of these three values!

i.e. no change = 0 emf

Recall:

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Electromagnetic Induction in a Loop


B Field

Current i

A diagram shows a 3 loop microcoil. The dimensions of the loops are 50 um by 40 um. If the B field is changing from 0 Tesla to 1 Tesla in 10 microseconds, find the emf across the leads.

Assuming a linear change with time for B:

Therefore:

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Example #1: Induction in a Microcoil


B Field

emf

The operation of a compass is well known.

The needle, which can be considered as a magnetic dipole, is held in an almost frictionless way.

When the needle starts at some arbitrary position, a magnetic torque will be developed, such that the needle will align itself with the Earth’s magnetic field.

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Magnetic Dipoles in Magnetic Fields

© N. Dechev, University of Victoria[Fig. 8.4 from ‘Foundations of MEMS’, Chang Liu]

External magnetic fields can be classified into two main categories:

- Uniform magnetic fields- Non-uniform magnetic fields

The effect of these fields on permanent ‘hard magnets’ is intuitive, in that they behave much the same way as a compass needle.

The effect of these fields on ‘soft magnetic’ materials, is interesting, in that these materials often exhibit ‘shape anisotropy’.

This means that ‘soft magnetic’ materials, when subjected to a magnetic field, will tend to develop a magnetic moment M, based on their shape, rather than the orientation of the field.

Practically, ‘soft magnets’ will develop a moment M, on their longitudinal axis, irrespective of of the direction of the induction field.

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Consider the diagram below:

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(a) No external magnetic field

permanent magnet soft magnet

(b) Uniform external magnetic field

Consider the diagram below:

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(c) Non-uniform external magnetic field

H1

H2

lecture 13: magnetic sensors & actuatorsmech466/mech466-lecture-13.pdfmagnetic field is removed,...

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